1. Field of the Invention
The present invention generally relates to measuring methods, methods for manufacturing optical elements, reference standards, and measuring devices.
2. Description of the Related Art
Interferometers are used to measure the shape of the surfaces of optical elements, such as lenses and mirrors. Such an interferometer obtains data on the shape of a measurement surface by emitting a measuring beam onto the measurement surface of an optical element (measurement object) and a reference surface and measuring the difference in position between them as interference fringes. Because the interferometer use light, it has higher measuring accuracy than measuring devices employing other measuring methods, such as contact type measuring devices.
The result of measurement by the interferometer contains measurement errors of the interferometer itself in addition to the data on the shape of the measurement surface. Thus, by calibrating the measurement data of the interferometer with the measurement error, the data on the shape of the measurement surface can be obtained. The measurement errors are classified into a measurement error in the direction normal to the measurement surface (system error) and a measurement error in the direction tangent to the measurement surface (distortion). The direction normal to the measurement surface means the normal direction at each point in the measurement surface. When the measurement surface is curved, the normal direction is determined corresponding to each point in the curved surface. Similarly, the direction tangent to the measurement surface means the tangent direction at each point in the measurement surface.
Japanese Patent Laid-Open No. 2002-213930 (U.S. Patent Laid-Open No. 2004/36890) discloses a method for calibrating a system error in which a plurality of measurement data are obtained by rotating a reference standard having substantially the same shape as a measurement surface and arithmetic processing is performed using the data. As will be described below, in the invention disclosed therein, the system error is determined by subtracting a rotationally asymmetric component and rotationally symmetric component of the shape data of the reference standard from the measurement data. Therefore, by calibrating the measurement data of the measuring device with the system error, the data on the shape of the measurement surface can be obtained. However, with this method, only the measurement error in the direction normal to the measurement surface can be determined, and the measurement error in the direction tangent to the measurement surface (distortion) cannot be determined.
On the other hand, Japanese Patent Laid-Open No. 2002-333305 discloses a method for calibrating distortion. More specifically, it discloses forming marks, serving as light-shielding portions, at specific coordinates on the optically effective area of a reference standard. From the measured coordinates of the marks and the true coordinates of the marks, the distortion of the measuring device is determined and calibrated.
As described above, a reference standard having marks is used only for calibration of distortion. Therefore, to calibrate a system error, a reference standard having no marks is needed. This increases the manufacturing costs. In addition, because the calibrations of the system error and distortion of the interferometer have to be performed in separate steps, the cycle time of a measurement sequence increases.